Question

in the diagram, $overline{kl}congoverline{nr}$ and $overline{jl}congoverline{mr}$. what additional information is needed to show $\triangle{jkl}cong\triangle{mnr}$ by sas?
$angle{j}congangle{m}$
$angle{l}congangle{r}$
$angle{k}congangle{n}$
$angle{r}congangle{k}$

Explanation:

Step1: Recall SAS congruence criterion

The Side - Angle - Side (SAS) congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
In \(\triangle{JKL}\) and \(\triangle{MNR}\), we are given that \(KL\cong NR\) and \(JL\cong MR\). The included angles for these pairs of sides are \(\angle{L}\) and \(\angle{R}\) respectively.

Step2: Determine the required angle

For \(\triangle{JKL}\cong\triangle{MNR}\) by SAS, we need \(\angle{L}\cong\angle{R}\) since they are the included angles between the given pairs of congruent sides.

Answer:

B. \(\angle{L}\cong\angle{R}\)